The Fifth of the Five Ways

[Belacqua]

from Wikipedia:

It must be emphasized that this argument is distinct from the design argument associated with William Paley and the Intelligent Design movement. The latter implicitly argue that objects in the world do not have inherent dispositions or ends, but, like Paley's watch, will not naturally have a purpose unless forced to do some outside agency.[24] The latter also focus on complexity and interworking parts as the effect needing explanation, whereas the Fifth Way takes as its starting point any regularity.[24] (E.g., [the Intelligent Design movement argues] that an eye has a complicated function therefore a design therefore a designer) but [Aquinas instead makes] an argument from final cause (e.g., that the pattern that things exist with a purpose itself allows us to recursively arrive at God as the ultimate source of purpose without being constrained by any external purpose).

the bolded parts I added for clarity

This part is good, too:

Proofs or Ways?

Many scholars and commenters caution against treating the Five Ways as if they were modern logical proofs. This is not to say that examining them in that light is not academically interesting.

Reasons include:

Purpose: The purpose of the Summa theologica "is to help Dominicans not enrolled in the university prepare for their priestly duties of preaching and hearing confessions"[25] by systematizing Catholic truth utilizing mainly Aristotelean tools.

Precis: Aquinas subsequently revisited the various arguments of the Five Ways in much greater detail. The simple list in the Summa theologica is not written to be clear (to a 21st-century reader) and complete, and should be considered a sketch or summary of the idea, suitable for presentation in a lecture or a quick browse.

Via negativa: Aquinas held that "we are unable to apprehend (the Divine substance) by knowing what it is. Yet we are able to have some knowledge of it by knowing what it is not." (SCG I.14) Consequently, to understand the Five Ways as Aquinas understood them we must interpret them as negative theology listing what God is not (i.e. not a moved mover, not a caused causer, etc.). It invites logical fallacy to use the statements as positive definitions rather than negative exclusions.[26]